To complete this table using equivalent ratios, let's analyze the relationship between sticks of butter and the number of cookies.

The initial ratio given is: $\frac{3 \text{ sticks of butter}}{24 \text{ cookies}}$

Step 1: Find the ratio of butter to cookies

The ratio simplifies as follows: $\frac{3}{24} = \frac{1}{8}$

So, for every stick of butter, there are 8 cookies.

Step 2: Solve for the missing values

1. Second row: We know there are 16 cookies, so we find the corresponding number of sticks of butter: $\frac{\text{sticks of butter}}{16 \text{ cookies}} = \frac{1}{8}$ Solving for sticks of butter: $\text{sticks of butter} = \frac{16}{8} = 2$

2. Third row: We know there are 5 sticks of butter, so we find the corresponding number of cookies: $\frac{5 \text{ sticks of butter}}{\text{cookies}} = \frac{1}{8}$ Solving for cookies: $\text{cookies} = 5 \times 8 = 40$

Final Table

Would you like more details or have any questions?

1. How would you find the missing values if only partial ratios were given?
2. What is an equivalent ratio, and why is it useful in real-life applications?
3. How can you scale ratios to solve larger or smaller quantities?
4. What happens to the ratio if we double the number of cookies but keep the same sticks of butter?
5. How can we verify that our answers are correct?

Tip: To find equivalent ratios, always check if the same simplified fraction applies across all values.